week-4 slide - large scale path loss
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Lecture 4: Large-Scale Path Loss
Chapter 4 – Mobile Radio Propagation:
Large-Scale Path Loss
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Last two lectures: Properties of cellular radio systems
Frequency reuse by using cells
Clustering and system capacity
System components - Mobile switching centers, base stations, mobiles, PSTN
Handoff strategies
Handoff margin, guard channels
Mobile Assisted Handoff
Umbrella cells
Hard and soft handoffs
Co-Channel Interference
Adjacent Channel Interference
Trunking and grade of service (GOS)
Cell splitting
Sectoring
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This lecture: Electromagnetic propagation
properties and hindrances.
What are reasons why wireless signals are hard
to send and receive?
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I. Problems Unique to Wireless (not wired) systems:
Paths can vary from simple line-of-sight to ones
that are severely obstructed by buildings,
mountains, and foliage.
Radio channels are extremely random and
difficult to analyze.
Interference from other service providers
out-of-band non-linear Tx emissions
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Interference from other users (same network)
CCI due to frequency reuse
ACI due to Tx/Rx design limitations & large #
users sharing finite BW
Shadowing
Obstructions to line-of-sight paths cause areas of
weak received signal strength
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Fading
When no clear line-of-sight path exists, signals are
received that are reflections off obstructions and
diffractions around obstructions
Multipath signals can be received that interfere with
each other
Fixed Wireless Channel → random & unpredictable
must be characterized in a statistical fashion
field measurements often needed to characterize radio
channel performance
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** The Mobile Radio Channel (MRC) has
unique problems that limit performance **
A mobile Rx in motion influences rates of
fading
the faster a mobile moves, the more quickly
characteristics change
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II. Radio Signal Propagation
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The smoothed line is the average signal
strength. The actual is the more jagged line.
Actual received signal strength can vary by
more than 20 dB over a few centimeters.
The average signal strength decays with
distance from the transmitter, and depends on
terrain and obstructions.
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Two basic goals of propagation modeling:
1) Predict magnitude and rate (speed) of received
signal strength fluctuations over short
distances/time durations
“short” → typically a few wavelengths (λ) or
seconds
at 1 GHz, λ = c/f = 3x108 / 1x109 = 0.3 meters
received signal strength can vary drastically by 30
to 40 dB
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small-scale fluctuations → called _____ (Chapter 5)
caused by received signal coming from a sum of
many signals coming together at a receiver
multiple signals come from reflections and
scattering
these signals can destructively add together by being
out-of-phase
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2) Predict average received signal strength for
given Tx/Rx separation
characterize received signal strength over distances
from 20 m to 20 km
Large-scale radio wave propagation model models
needed to estimate coverage area of base station
in general, large scale path loss decays gradually
with distance from the transmitter
will also be affected by geographical features like
hills and buildings
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Free-Space Signal Propagation
clear, unobstructed line-of-sight path → satellite and
fixed microwave
Friis transmission formula → Rx power (Pr) vs. T-R
separation (d)
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where
Pt = Tx power (W)
G = Tx or Rx antenna gain (unitless)
relative to isotropic source (ideal antenna which
radiates power uniformly in all directions)
in the __far field__ of an antenna (beyond a few meters)
Effective Isotropic Radiated Power (EIRP)
EIRP = PtGt
Represents the max. radiated power available
from a Tx in the direction of max. antenna gain,
as compare to an isotropic radiator
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λ = wavelength = c / f (m). A term is related to
antenna gain.
So, as frequency increases, what happens to the
propagation characteristics?
L = system losses (antennas, transmission lines
between equipment and antennas, atmosphere, etc.)
unitless
L = 1 for zero loss
L > 1 in general
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d = T-R separation distance (m)
Signal fades in proportion to d2
We can view signal strength as related to the
density of the signal across a large sphere.
This is the surface area of a sphere with radius d.
So, a term in the denominator is related to distance
and density of surface area across a sphere.
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⇒ Path Loss (PL) in dB:
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d2 → power law relationship
Pr decreases at rate of proportional to d2
Pr decreases at rate of 20 dB/decade (for line-of-
sight, even worse for other cases)
For example, path loses 20 dB from 100 m to 1 km
Comes from the d2 relationship for surface area.
Note: Negative “loss” = “gain”
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Example:
Path loss can be computed in terms of a link budget
calculation.
Compute path loss as a sum of dB terms for the
following:
Unity gain transmission antenna.
Unity gain receiving antenna.
No system losses
Carrier frequency of 3 GHz
Distance = 2000 meters
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Close in reference point (do) is used in large-scale models
do : known received power reference point - typically 100 m or
1 km for outdoor systems and 1 m for indoor systems
df : far-field distance of antenna, we will always work problems
in the far-field
D: the largest physical linear dimension of antenna
22 f f f
Dd d D d
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Reference Point Example:
Given the following system characteristics for large-
scale propagation, find the reference distance do.
Received power at do = 20 W
Received power at 5 km = 13 dBm
Using Watts:
Using dBm:
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III. Reflections
There are three basic propagation mechanisms
in addition to line-of-sight paths
Reflection - Waves bouncing off of objects of large
dimensions
Diffraction - Waves bending around sharp edges of
objects
Scattering - Waves traveling through a medium
with small objects in it (foliage, street signs, lamp
posts, etc.) or reflecting off rough surfaces
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Reflection occurs when RF energy is incident upon
a boundary between two materials (e.g air/ground)
with different electrical characteristics
Permittivity µ
Permeability ε
Conductance σ
Reflecting surface must be large relative to λ of RF
energy
Reflecting surface must be smooth relative to λ of
RF energy
“specular” reflection
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What are important reflecting surfaces for
mobile radio?
Fresnel reflection coefficient → Γ
describes the magnitude of reflected RF energy
depends upon material properties, polarization, &
angle of incidence
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IV. Ground Reflection (2-Ray) Model
Good for systems that use tall towers (over 50 m
tall)
Good for line-of-sight microcell systems in urban
environments
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ETOT is the electric field that results from a combination of a direct line-of-sight path and a ground reflected path
is the amplitude of the electric field at distance d
ωc = 2πfc where fc is the carrier frequency of the signal
Notice at different distances d the wave is at a different phase because of the form similar to
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For the direct path let d = d’ ; for the reflected path
d = d” then
for large T−R separation : θi goes to 0 (angle of incidence
to the ground of the reflected wave) and
Γ = −1
Phase difference can occur depending on the phase
difference between direct and reflected E fields
The phase difference is θ∆ due to Path difference , ∆ =
d”− d’, between
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From two triangles with sides d and (ht + hr) or (ht – hr)
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∆ can be expanded using a Taylor series
expansion
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which works well for d >> (ht + hr), which means
and are small
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the phase difference between the two arriving
signals is
0 0
0 0
2
( ) 2 sin2
20.3 rad
2
2( ) 2 V/m
TOT
r t
r tTOT
E dE t
d
h h
d
E d h h kE t
d d d
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For d0=100meter, E0=1, fc=1 GHz, ht=50 meters, hr=1.5 meters, at t=0
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note that the magnitude is with respect to a
reference of E0=1 at d0=100 meters, so near 100
meters the signal can be stronger than E0=1
the second ray adds in energy that would have been
lost otherwise
for large distances it can be shown
that
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V. Diffraction
RF energy can propagate:
around the curved surface of the Earth
beyond the line-of-sight horizon
Behind obstructions
Although EM field strength decays rapidly as
Rx moves deeper into “shadowed” or
obstructed (OBS) region
The diffraction field often has sufficient
strength to produce a useful signal
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Huygen’s principle says points on a wavefront
can be considered sources for additional
wavelets.
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The wavefront on top of an obstruction generates
secondary (weaker) waves.
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The difference between the direct path and
diffracted path, call excess path length
Fresnel-Kirchoff diffraction parameter
The corresponding phase difference
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The excess total path length traversed by a ray
passing through each circle is nλ/2
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The diffraction gain due to the presence of a knife
edge, as compared the the free space E-field
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Eq. 4.61.a –e
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Eq. 4.54
Eq. 4.56
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Eq. 4.56
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VI. Scattering
Received signal strength is often stronger than that
predicted by reflection/diffraction models alone
The EM wave incident upon a rough or complex
surface is scattered in many directions and provides
more energy at a receiver
energy that would have been absorbed is instead reflected to
the Rx.
Scattering is caused by trees, lamp posts, towers, etc.
flat surface → EM reflection (one direction)
rough surface → EM scattering (many directions)
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VII. Path Loss Models
We wish to predict large scale coverage using
analytical and empirical (field data) methods
It has been repeatedly measured and found that
Pr @ Rx decreases logarithmically with
distance
∴ PL (d) = (d / do )n where n : path loss exponent or
PL (dB) = PL (do ) + 10 n log (d / do )
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“bar” means the average of many PL values at a given value of d (T-R sep.)
n depends on the propagation environment
“typical” values based on measured data
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At any specific d the measured values vary
drastically because of variations in the
surrounding environment (obstructed vs. line-
of-sight, scattering, reflections, etc.)
Some models can be used to describe a
situation generally, but specific circumstances
may need to be considered with detailed
analysis and measurements.
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Log-Normal Shadowing
PL (d) = PL (do ) + 10 n log (d / do ) + Xσ
describes how the path loss at any specific location may vary
from the average value
has a the large-scale path loss component we have already
seen plus a random amount Xσ.
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Xσ : zero mean Gaussian random variable, a “bell curve”
σ is the standard deviation that provides the second
parameter for the distribution
takes into account received signal strength variations
due to shadowing
measurements verify this distribution
n & σ are computed from measured data for different
area types
any other path loss models are given in your book.
That correlate field measurements with models for different
types of environments.
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